Browsing by Author "Petras, Ivo"

Now showing 1 - 6 of 6

Citation Count: Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo, "Fractional Bateman-Feshbach Tikochinsky Oscillator", Communications in Theoretical Physics, 61, No. 2, pp. 221-225, (2014).
Fractional Bateman-Feshbach Tikochinsky Oscillator
(IOP Publishing LTD, 2014) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; 56389
In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman-Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grunwald-Letnikov approach, which is power series expansion of the generating function.
Citation Count: Baleanu, D...et al. (2012). "FRACTIONAL EULER-LAGRANGE EQUATION OF CALDIROLA-KANAI OSCILLATOR, Romanian Reports In Physics, Vol. 64, pp. 1171-1177.
Fractional Euler-Lagrange Equation of Caldirola-Kanai Oscillator
(Editura Academiei Romane, 2012) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; Elagan, S.; Bilgen, A.; 56389
A study of the fractional Lagrangian of the so-called Caldirola-Kanai oscillator is presented. The fractional Euler-Lagrangian equations of the system have been obtained, and the obtained Euler-Lagrangian equations have been studied numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.
Citation Count: Baleanu, Dumitru...et al. (2012). "Fractional Pais-Uhlenbeck Oscillator", International Journal of Theoretical Physics, Vol. 51. No. 4. pp. 1253-1258.
Fractional Pais-Uhlenbeck Oscillator
(Springer, 2012) Baleanu, Dumitru; Petras, Ivo; Asad, Jihad H.; Pilar Velasco, Maria; 56389; 56389
In this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.
Citation Count: Baleanu, D., Asad, J.H., Petras, I. (2012). Fractional-order two-electric pendulum. Romanian Reports in Physics, 64(4), 907-914.
Fractional-order two-electric pendulum
(Editura Acad Romane, 2012) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo
In this paper we study the fractional Lagrangian of the two-electric pendulum. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation analytically, and numerically. The numerical method used here is based on Grunwald-Letnikov definition of left and right fractional derivatives
Citation Count: Zaman, S.F., Baleanu, D., Petras, I. (2016). A fractional finite difference inclusion. Journal of Computational Analysis and Applications, 19(2), 551-560. http://dx.doi.org/10.1515/fca-2016-0028
Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the mittag-leffler function
(Walter De Gruyter GMBH, 2016) Zaman, Sharif F.; Baleanu, Dumitru; Petras, Ivo
The new fractional calculus modeling based on Mittag-Leffler function has been employed to generate a better fit model to analyze the ZLC desorption curves for para-xylene diffusion in ZSM-5 zeolites. The diffusivity values generated herewith at 100, 125 and 150 degrees C are reported as 4.4 x 10(-13), 4.98 x 10(-13) and 5.2 x 10(-13) m(2)/s, respectively. The activation energy for this diffusion process is found 4.2 kJ/mol and diffusion proportional constant (D-0) is 1.85 x 10(-12) m(2)/s. The simplified model for ZLC response can be a better way to treat desorption data in ZLC experiments.
Citation Count: Baleanu, D., Asad, J.H., Petras, I. (2015). Numerical solution of the fractional Euler-Lagrange's equations of a thin elastica model. Nonlinear Dynamics, 81(1-2), 97-102. http://dx.doi.org/10.1007/s11071-015-1975-7
Numerical solution of the fractional Euler-Lagrange's equations of a thin elastica model
(Springer, 2015) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo
In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange's equations of the system numerically. The numerical study is based on Grunwald-Letnikov approach, which is power series expansion of the generating function. We present an illustrative example of the proposed numerical model of the system.